Intense LASER interactions with H 2 + and D 2 + : A Computational Project
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Intense LASER interactions with H2
+ and D2+:
A Computational Project
Ted Cackowski
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Project Description
Assisting the multiple-body-mechanics group at KSU with calculations of H2
+/D2+
behavior under the influence of a short, yet intense laser pulse.
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Motivation
To explore the validity of the Axial Recoil Approximation Exploring the quantum mechanics of
H2+/D2
+ in a time-varying electric field under various experimental conditions
Exploring the quantum dynamics there afterward
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Modes of Operation
Schrödinger's Equation
and the associated quantum mechanics Fortran 90/95
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Process Overview
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Physical Situation
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Scales of Physical Interest
Laser Intensity: ~1E14 watts/cm2
Pulse Length: ~7E -15 s (femtoseconds) Frequency: 790E-9 m (nanometers) H2/D2 Nuclear Separation:
~3E-10 m (angstroms)
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Diatomic Hydrogen
Two protons, two electrons Born-Oppenheimer Approximation
First Electrons, then Nuclei
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Figure 1
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H2+ Molecule
There are two separate pulses. Ionizing pulse gives us our
computational starting point Franck-Condon Approximation
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Figure 2
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Note on Completeness
The Overlap Integral
Where, |FCV|2 are bound/unbound probabilities Unavoidable dissociation by ionization Controlled dissociation
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Mechanics
The second pulse is the dissociating pulse.
We now have the Hamiltonian of interest Dipole Approximation
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Linear Methods
We expand initialonto an orthonormal basis Overlap integral / Fourier’s trick
We then generate the matrix H as in
Propagate the vector through time using an arsenal of numerical techniques
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Data Production
After producing a nuclear wave function associated with a particular dissociation channel, any physical observable can be predicted.
“Density Plots” are probability density plots (Ψ*Ψ)
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Channels
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Notable Observables
Angular distribution of dissociationas it depends on: Pulse Duration Pulse Intensity Carrier Envelope Phase (CEP)
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My Work
Computational Oversight Two Fortran Programs
First: Calculate the evolution of the wave function when the Electric field is non-negligible
Second: Calculate the evolution of the wave function when the Electric field is negligible
Produce measurable numbers
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Afore Mentioned Figure
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Alignment VS. Pulse DurationFor H2+, CEP Zero, 1E13
0
1
2
3
4
5
0 50 100 150
Pulse Length (Femtoseconds)
Per
cent
Cha
nge
in
<Cos
(thet
a)**
2>
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Alignment VS. Electric Field StrengthFor H2+, 5fs, CEP Zero
1010.5
1111.5
1212.5
1313.5
4.00E+13
5.00E+13
6.00E+13
7.00E+13
8.00E+13
9.00E+13
1.00E+14
1.10E+14
Intensity (Watts/(cm^2))
Per
cent
Cha
nge
in
<Cos
(thet
a)**
2>
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Alignment VS. Electric Field StrengthFor H2+, 10fs, CEP Zero
10.25
10.5
10.75
11
4.00E+13
5.00E+13
6.00E+13
7.00E+13
8.00E+13
9.00E+13
1.00E+14
1.10E+14
Intensity (Watts/(cm^2))
Per
cent
cha
nge
in
<Cos
(thet
a)**
2>
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Alignment VS. Carrier Envelope PhaseFor D2+, 5fs, 1E14
89
10111213141516
0 0.5 1 1.5 2
CEP ( Pi )
Per
cent
cha
nge
in
<Cos
(thet
a)**
2>
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Conclusions
Rotational inertia plays an important role Pulse intensity is critical Further analysis will be required for
pulse length and CEP
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Future Work
Simulate H2+ under various CEP initial
conditions Confidence Testing Data Interpretation Connect with JRM affiliates
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Special Group Thanks
Dr. Esry Fatima Anis Yujun Wang Jianjun Hua Erin Lynch
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Special REU Thanks
Dr. Weaver Dr. Corwin Participants Jane Peterson
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Bibliography
Figure 1 from Max Planck institute for Quantum Optics website
Figure 2 from Wikipedia, “Frank-Condon”
http://images.google.com/imgres?imgurl=http://www.mpq.mpg.de/~haensch/grafik/3DdistributionD.gif&imgrefurl=http://www.mpq.mpg.de/~haensch/htm/Research.htm&h=290&w=420&sz=24&hl=en&start=0&um=1&tbnid=rOBflIUYzSm7xM:&tbnh=86&tbnw=125&prev=/images%3Fq%3DH2%252B%26svnum%3D10%26um%3D1%26hl%3Den%26sa%3DN
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